Mathematics question...?

This doesn't happen in your first couple years at undergrad. Normally in your late second year or early third years you start to take proof based classes.

If you are interested now, I know of a book that made me fall in love with the subject and want to be a 'pure' mathematician.

The book I would recommend is:

Set Theory and Metric Spaces

By Irving Kaplansky ISBN: 0821826948

As I said this book made me fall in love with the subject of mathematics and want to do that as opposed to something else. I took this in the beginning of my 3rd year of undergrad.

It really isn't too hard to read, however it is kind of hard to start writing proofs on your own without someone to guide you. You may go around and ask some teachers if they have an introductory course for advanced mathematics, like I took, ask if you just can sit in or ask to take it pass/fail.

Or perhaps you can find someone that is willing to take you under their wing and personally guide you in becoming a mathematician.

Set theory is good to learn how to read and write proofs and it is enlightening as to how useful and powerful the subject is. It makes a good solid introduction to the things that will follow. However it is only the beginning.

There are 4 main areas of pure mathematics that you should be familiar with. If you intend on going to graduate school and getting a PhD then you must choose one of them to master in. (Actually you choose a sub-category of a couple in some crazy intersection of these different theories.)

The 4 areas are:

Abstract Algebra

Real Analysis

Topology

Complex Analysis

Some good first year books that I had are:

Abstract Algebra, An Introduction

2nd edition

Thomas Hungerford

ISBN: 0-03-010559

Principles of Mathematical Analysis

3rd edition

Walter Rudin

ISBN: 0-07-085613-3

Topology

James R. Munkres

ISBN: 0131816292

Complex Variables and Applications

James Ward Brown & Ruel V. Churchill

ISBN: 0072872527

Any of these, I feel, provides a good, well written introduction to the subject and shows you how to write proofs and gives you a good understanding of the layout of the subject and a taste of things to come. See if your library has them, perhaps you could do some reading on some stuff on the internet, and get a feel. In the end you really do need some book so that you can see the whole layout and not just the snippets and 'important parts'.

Personally I'm fond of Algebra. I like how accessible the topic is and the types of questions one asks and answers with the subject. Depending on what you find interesting will guide you to really like one topic and get to like it.

Good luck and feel free to ask me any questions you might have!

Writing mathematical proofs is quite simple. Most books aren't about writing proofs since there isn't one perfect process to writing a proof.

However, I would give you the following steps:

1. Think about the entire process through which something is going to be proved.

2. If you are going to prove things are every step... say f1,f2,..fm, then make sure that you can prove these by any means necessary.

3. Please make sure that a uniform method is used i.e. if possible use similar approaches for proving f1..fm.

4. Using the series of conclusions, c1..cm, prove the final result.

This is not the best way to probably write proofs since I believe that most proofs come from sheer creativity. You need not take a Masters for that.

Here is a link to understand the standard method of writing mathematical proofs:

http://zimmer.csufresno.edu/~larryc/proofs/proofs....

Most of the time though, you need to believe in what you want to prove and just look for the means to prove it.

Hope this helps.

A mathematical proof is a set of steps based in mathematical fact that use deductive logic.

This will not help you :)

I will look up some sites that might help.

It would help to know what topic you are studying. Geometric proofs are often different then algebraic proofs.

Geometric proofs

http://www.sparknotes.com/math/geometry3/geometric...

http://www.themathlab.com/geometry/mathcourt/write...

In the mathlab site click on the examples

The difference between a two column proof and a paragraph proof is just how you write it. The concept is the same. How do you know this _______ is true?

http://pass.maths.org.uk/issue7/features/proof1/in...

It also may help to post examples of questions here to answers to get the idea of how to prove things by seeing others do it.

I was very confused about proofs when I started my degree in mathematics. It is a concept you have to grasp. Seeing alot of examples may get you to start to understand how people are making connections.

So you're studying maths at college degree level? If you feel you're not learning enough about proof, or rigour? There's no easy way to learn it, it should be covered in pretty much all the courses you'd study at that level. And in a way, if you're not learning it now, then what kinda stuff are you studying?

what mathematical statements do u actually want to prove? or do you mean u want to learn about proving methods like, by induction, inspection etc..